To solve this equation, we'll first simplify the left side of the equation by distributing the 9/11:

9/11 x - 9/11 2/3 = 5011

Simplify further:

9/11 * x - 6/11 = 5011

Now, we'll isolate the x term by adding 6/11 to both sides:

9/11 * x = 5011 + 6/11

9/11 * x = 5011 + 66/11

9/11 * x = 5011 + 66

9/11 * x = 5077

Now, multiply both sides by the reciprocal of 9/11, which is 11/9:

x = 5077 * 11/9

x = 6217

Therefore, the solution to the first equation is x = 6217.

Now, let's solve the second equation. We'll first simplify the left side by distributing the 12:

12 * (x - 2/15) = 6

12x - 24/15 = 6

Simplify further:

12x - 8/5 = 6

Now, isolate the x term by adding 8/5 to both sides:

12x = 6 + 8/5

12x = 30/5 + 8/5

12x = 38/5

Now, divide by 12 to solve for x:

x = 38/5 / 12

x = 38/5 * 1/12

x = 38/60

x = 19/30

Therefore, the solution to the second equation is x = 19/30.

In conclusion, the solutions to the given equations are x = 6217 and x = 19/30.